Abstract

Relationships between subsurface damage (SSD) depth and peak to valley surface roughness (Rt) have been widely studied and present a major interest for an easy assessment of the SSD depth. We look at the relation between SSD depth and other surface roughness parameters using the Abbott-Firestone curve on a large campaign of grinding tests (with different abrasive grain size, grinding speed and grinding mode). The results reveal that Abbott-Firestone parameters are better for an assessment of SSD depth and that relationships between SSD depth and surface roughness are not universal but depend on the grinding process.

mean and maximal error between the measured SSD and the estimated SSD for each surface roughness
parameter, calculated for 3 subsets of experiments (rough and intermediate grinding, finishing, and
lapping).

Table 3 Summary of measured SSD and roughness parameters for fused silica samples Batches A-E except
for batch D errors on SSD depth are less than 3%; errors on roughness measurements are less than
10%, see §3.1 for further details

Table 3

Summary of measured SSD and roughness parameters for fused silica samples Batches A-E except
for batch D errors on SSD depth are less than 3%; errors on roughness measurements are less than
10%, see §3.1 for further details

batch

sample number

SSD depth (µm)

Rtmax (µm)

Ra (µm)

Rt (µm)

Rq (µm)

Rku (µm)

δ (µm)

Rk (µm)

Rpk (µm)

Rvk (µm)

Mr1 (%)

Mr2 (%)

A

1

69.4

19.1

1.4

14.1

1.9

8.3

3.2

2.3

0.4

4.1

4.1

73.0

2

69.0

18.2

1.4

13.8

1.9

8.6

3.3

2.1

0.4

4.3

4.3

72.6

3

70.4

13.2

1.1

11.4

1.5

8.5

2.6

1.8

0.3

3.3

3.9

72.9

4

71.6

21.6

1.2

13.8

1.8

9.5

3.1

1.9

0.4

3.9

4.7

72.6

5

68.0

19.0

1.2

13.9

1.8

10.3

3.2

1.8

0.4

4.0

5.0

72.2

6

78.0

10.2

0.5

7.3

0.8

18.0

1.7

0.7

0.1

2.0

5.3

76.4

7

89.7

16.5

0.6

8.2

1.0

14.6

1.9

0.8

0.2

2.3

5.1

76.1

8

63.1

16.7

0.9

11.3

1.3

11.1

2.4

1.7

0.5

2.9

7.4

79.6

9

84.6

14.8

0.9

11.7

1.4

12.8

2.7

1.3

0.6

3.4

6.2

76.6

10

77.2

14.7

0.8

9.2

1.2

10.0

2.1

1.3

0.3

2.8

5.0

76.2

11

74.8

15.6

0.9

10.2

1.3

11.2

2.4

1.3

0.3

3.0

5.3

74.1

12

82.0

12.1

0.8

8.8

1.2

9.8

2.1

1.3

0.3

2.8

5.0

74.5

13

76.3

11.8

0.8

9.0

1.2

11.2

2.1

1.4

0.3

2.7

5.5

75.8

B

1

44.1

7.1

0.3

4.4

0.5

9.2

0.8

0.9

0.2

0.8

5.4

83.8

2

47.3

13.9

0.4

6.5

0.6

16.6

1.2

1.0

0.3

1.2

6.1

82.2

3

43.1

4.9

0.2

3.3

0.3

14.6

0.5

0.5

0.2

0.5

7.0

81.6

4

44.7

11.4

0.8

9.1

1.1

6.1

1.7

2.2

0.5

1.9

5.0

82.2

5

52.2

16.4

1.4

13.0

1.9

4.4

2.7

4.1

0.8

2.9

6.3

84.2

C

1

37.1

6.4

0.3

4.3

0.5

15.7

0.8

0.9

0.2

0.8

6.0

83.0

2

50.5

7.5

0.3

5.1

0.4

31.1

1.0

0.5

0.1

0.9

5.7

80.4

3

54.7

9.8

0.4

6.0

0.6

17.2

1.2

0.7

0.2

1.3

5.8

79.2

4

40.6

8.0

0.5

5.9

0.7

11.7

1.2

1.0

0.2

1.3

5.3

78.5

5

39.9

9.2

0.4

4.3

0.5

9.0

0.8

1.0

0.2

0.9

5.0

81.4

6

43.2

5.9

0.2

3.9

0.4

19.0

0.7

0.5

0.2

0.8

5.6

80.6

7

46.2

15.1

0.4

6.1

0.6

16.9

1.2

0.7

0.4

1.3

6.4

79.7

8

42.6

7.7

0.4

5.3

0.6

13.0

1.1

0.8

0.2

1.3

5.1

78.0

9

43.3

8.4

0.4

5.8

0.6

14.8

1.2

0.8

0.2

1.4

5.3

78.0

10

43.6

7.7

0.4

5.6

0.6

16.4

1.1

0.7

0.1

1.3

5.1

77.9

11

45.9

7.9

0.4

5.3

0.6

16.4

1.1

0.7

0.1

1.3

5.2

78.2

D

1

8.2

1.9

0.03

0.6

0.04

17.3

0.09

0.09

0.04

0.06

9.5

88.1

2

4.8

1.9

0.02

0.4

0.03

12.5

0.06

0.07

0.04

0.03

9.9

89.1

3

10.8

0.8

0.02

0.4

0.03

10.1

0.06

0.07

0.04

0.04

10.2

88.7

4

11.5

1.9

0.04

0.7

0.06

29.5

0.1

0.1

0.06

0.06

10.2

87.6

5

20.5

2.0

0.02

0.5

0.03

33.1

0.06

0.08

0.03

0.04

10.0

88.8

E

1

26.1

6.4

0.4

4.3

0.5

5.5

0.8

1.2

0.3

0.8

8.0

85.7

2

18.8

7.2

0.7

6.0

0.9

3.7

1.2

2.1

0.6

1.1

8.2

87.4

3

24.2

8.1

0.7

6.5

0.9

3.5

1.3

2.3

0.7

1.2

8.0

87.7

4

19.8

6.8

0.5

5.0

0.7

4.2

0.9

1.6

0.5

0.8

8.4

87.7

5

7.6

3.5

0.3

2.4

0.3

3.6

0.4

0.8

0.2

0.4

8.3

87.7

6

41.6

12.2

1.0

8.8

1.3

3.4

1.8

3.2

1.0

1.5

8.4

87.9

7

25.4

9.8

0.8

7.6

1.1

3.8

1.5

2.6

0.7

1.4

8.1

87.4

8

12.3

5.5

0.3

3.4

0.4

4.1

0.6

1.0

0.3

0.5

8.2

87.8

9

20.7

12.5

0.7

6.8

1.0

5.4

1.4

1.9

0.7

1.6

7.9

84.4

Tables (3)

Table 1

Summary of grinding parameters for fused silica samples Batches A-C

batch

sample number

wheel grit(aperture
rangein µm)

cutting
speed(m/min)

feed
rate(mm/tr)

depth of
cut(mm)

A

1

D126(125/106)

1167.50

0.0275

0.75

2

1167.50

0.0275

0.75

3

1167.50

0.0275

0.75

4

1167.50

0.0275

0.75

5

1167.50

0.0275

0.75

6

785.00

0.0150

0.50

7

785.00

0.0150

1.00

8

1550.00

0.0150

0.50

9

1550.00

0.0150

1.00

10

1550.00

0.0400

0.50

11

1550.00

0.0400

1.00

12

785.00

0.0400

1.00

13

785.00

0.0400

0.50

B

1

D91(90/75)

1167.50

0.0250

0.70

2

785.00

0.0400

1.00

3

1550.00

0.0100

0.40

4

1167.50

0.0250

0.70

5

1167.50

0.0250

0.70

C

1

D64(63/53)

1550.00

0.0100

0.40

2

1550.00

0.0100

1.00

3

1550.00

0.0400

1.00

4

1550.00

0.0400

0.40

5

785.00

0.0100

0.40

6

785.00

0.0100

1.00

7

785.00

0.0400

1.00

8

785.00

0.0400

0.40

9

1167.50

0.0250

0.70

10

1167.50

0.0250

0.70

11

1167.50

0.0250

0.70

Table 2

Summary of grinding parameters for fused silica samples Batches D-E

batch

sample number

wheel grit(range in
µm)supplier data

cutting speed (m/min)

workpiece rotation speed (m/min)

feed rate (mm/tr)

depth of cut (mm)

D

1

D25(20/30)

2356.19

−16.00

1.67E-06

0.10

2

2356.19

−16.00

1.67E-06

0.10

3

2356.19

−16.00

1.67E-06

0.10

4

3141.59

−16.00

1.25E-06

0.10

5

2356.19

−12.00

1.67E-06

0.10

Table 3

Summary of measured SSD and roughness parameters for fused silica samples Batches A-E except
for batch D errors on SSD depth are less than 3%; errors on roughness measurements are less than
10%, see §3.1 for further details